HW Solutions Stat 59

HW Solutions Stat 59 - eij i j=1 j=2 j=3 j=4 j=5 j=6 j=7...

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e ij : i j = 1 j = 2 j = 3 j = 4 j = 5 j = 6 j = 7 j = 8 1 . 071 . 054 . 230 . 054 . 071 . 071 . 054 . 247 2 . 105 . 038 . 138 . 038 . 105 . 439 . 214 . 041 3 . 071 . 230 . 138 . 071 . 008 . 054 . 071 . 222 4 . 036 . 018 . 349 . 107 . 080 . 153 . 010 . 204 i j = 9 j = 10 j = 11 j = 12 j = 13 j = 14 j = 15 j = 16 1 . 168 . 071 . 230 . 071 . 071 . 230 . 054 . 071 2 . 041 . 214 . 263 . 163 . 038 . 138 . 105 . 038 3 . 163 . 230 . 071 . 033 . 230 . 106 . 008 . 138 4 . 153 . 186 . 061 . 128 . 010 . 085 . 240 . 167 b. r = . 971 c. H 0 : all σ 2 i are equal ( i = 1 , 2 , 3 , 4), H a : not all σ 2 i are equal. ˜ Y 1 = . 6021, ˜ Y 2 = . 7782, ˜ Y 3 = 1 . 0603, ˜ Y 4 = 1 . 2173, MSTR = . 001214, MSE = . 01241, F L = . 001214 /. 01241 = . 10, F ( . 95; 3, 60) = 2 . 76. If F L 2 . 76 conclude H 0 , otherwise H a . Conclude H 0 . 18.20. i : 1 2 3 4 s i : 1 . 09354 1 . 99583 3 . 23973 5 . 37858 w i : . 83624 . 25105 . 09528 . 034567 H 0 : all µ i are equal ( i = 1 , 2 , 3 , 4), H a : not all µ i are equal. SSE w ( F ) = 60, df F = 60, SSE w ( R ) = 213 . 9541, df R = 63, F w = [(213 . 9541 60) / 3] ÷ (60 / 60) = 51 . 32, F ( . 99; 3, 60) = 4 . 13. If F w 4 . 13 conclude H 0 , otherwise H a . Conclude H a . 18.23. a. H 0 : all µ i are equal ( i = 1 , 2 , 3 , 4), H a : not all µ i are equal. MSTR = 470 . 8125, MSE = 28 . 9740, F R = 470 . 8125 / 28 . 9740 = 16 . 25, F ( . 95; 2 , 24) = 3 . 40. If
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